Optimal. Leaf size=24 \[ -5+e^{e^{e^x+\left (2+e^{e^{e^x}}\right )^2}}+3 x \]
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Rubi [F] time = 1.36, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \left (3+\exp \left (4+4 e^{e^{e^x}}+e^{2 e^{e^x}}+e^{4+4 e^{e^{e^x}}+e^{2 e^{e^x}}+e^x}+e^x\right ) \left (e^x+4 e^{e^{e^x}+e^x+x}+2 e^{2 e^{e^x}+e^x+x}\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=3 x+\int \exp \left (4+4 e^{e^{e^x}}+e^{2 e^{e^x}}+e^{4+4 e^{e^{e^x}}+e^{2 e^{e^x}}+e^x}+e^x\right ) \left (e^x+4 e^{e^{e^x}+e^x+x}+2 e^{2 e^{e^x}+e^x+x}\right ) \, dx\\ &=3 x+\operatorname {Subst}\left (\int \exp \left (4+4 e^{e^x}+e^{2 e^x}+e^{4+4 e^{e^x}+e^{2 e^x}+x}+x\right ) \left (1+4 e^{e^x+x}+2 e^{2 e^x+x}\right ) \, dx,x,e^x\right )\\ &=3 x+\operatorname {Subst}\left (\int e^{4+4 e^x+e^{2 x}+e^{\left (2+e^x\right )^2} x} \left (1+4 e^x x+2 e^{2 x} x\right ) \, dx,x,e^{e^x}\right )\\ &=3 x+\operatorname {Subst}\left (\int \left (e^{4+4 e^x+e^{2 x}+e^{\left (2+e^x\right )^2} x}+4 e^{4+4 e^x+e^{2 x}+x+e^{\left (2+e^x\right )^2} x} x+2 e^{4+4 e^x+e^{2 x}+2 x+e^{\left (2+e^x\right )^2} x} x\right ) \, dx,x,e^{e^x}\right )\\ &=3 x+2 \operatorname {Subst}\left (\int e^{4+4 e^x+e^{2 x}+2 x+e^{\left (2+e^x\right )^2} x} x \, dx,x,e^{e^x}\right )+4 \operatorname {Subst}\left (\int e^{4+4 e^x+e^{2 x}+x+e^{\left (2+e^x\right )^2} x} x \, dx,x,e^{e^x}\right )+\operatorname {Subst}\left (\int e^{4+4 e^x+e^{2 x}+e^{\left (2+e^x\right )^2} x} \, dx,x,e^{e^x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 31, normalized size = 1.29 \begin {gather*} e^{e^{4+4 e^{e^{e^x}}+e^{2 e^{e^x}}+e^x}}+3 x \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.63, size = 242, normalized size = 10.08 \begin {gather*} {\left (3 \, x e^{\left ({\left ({\left (e^{\left (3 \, x\right )} + 4 \, e^{\left (2 \, x\right )}\right )} e^{\left (2 \, e^{x}\right )} + e^{\left (2 \, x + 2 \, e^{x} + 2 \, e^{\left (e^{x}\right )}\right )} + 4 \, e^{\left (2 \, x + 2 \, e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-2 \, x - 2 \, e^{x}\right )}\right )} + e^{\left ({\left ({\left (e^{\left (3 \, x\right )} + 4 \, e^{\left (2 \, x\right )}\right )} e^{\left (2 \, e^{x}\right )} + e^{\left ({\left ({\left (e^{\left (3 \, x\right )} + 4 \, e^{\left (2 \, x\right )}\right )} e^{\left (2 \, e^{x}\right )} + e^{\left (2 \, x + 2 \, e^{x} + 2 \, e^{\left (e^{x}\right )}\right )} + 4 \, e^{\left (2 \, x + 2 \, e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-2 \, x - 2 \, e^{x}\right )} + 2 \, x + 2 \, e^{x}\right )} + e^{\left (2 \, x + 2 \, e^{x} + 2 \, e^{\left (e^{x}\right )}\right )} + 4 \, e^{\left (2 \, x + 2 \, e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-2 \, x - 2 \, e^{x}\right )}\right )}\right )} e^{\left (-{\left ({\left (e^{\left (3 \, x\right )} + 4 \, e^{\left (2 \, x\right )}\right )} e^{\left (2 \, e^{x}\right )} + e^{\left (2 \, x + 2 \, e^{x} + 2 \, e^{\left (e^{x}\right )}\right )} + 4 \, e^{\left (2 \, x + 2 \, e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-2 \, x - 2 \, e^{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (2 \, e^{\left (x + e^{x} + 2 \, e^{\left (e^{x}\right )}\right )} + 4 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + e^{x}\right )} e^{\left (e^{x} + e^{\left (2 \, e^{\left (e^{x}\right )}\right )} + e^{\left (e^{x} + e^{\left (2 \, e^{\left (e^{x}\right )}\right )} + 4 \, e^{\left (e^{\left (e^{x}\right )}\right )} + 4\right )} + 4 \, e^{\left (e^{\left (e^{x}\right )}\right )} + 4\right )} + 3\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 23, normalized size = 0.96
method | result | size |
default | \(3 x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}+4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+{\mathrm e}^{x}+4}}\) | \(23\) |
risch | \(3 x +{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{x}}}+4 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+{\mathrm e}^{x}+4}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 22, normalized size = 0.92 \begin {gather*} 3 \, x + e^{\left (e^{\left (e^{x} + e^{\left (2 \, e^{\left (e^{x}\right )}\right )} + 4 \, e^{\left (e^{\left (e^{x}\right )}\right )} + 4\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.36, size = 25, normalized size = 1.04 \begin {gather*} 3\,x+{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^x}}}\,{\mathrm {e}}^{4\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.73, size = 27, normalized size = 1.12 \begin {gather*} 3 x + e^{e^{e^{x} + e^{2 e^{e^{x}}} + 4 e^{e^{e^{x}}} + 4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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